The measurement of a rotational speed, which is required for many machines and systems in technology, is physically equivalent to the measurement of angular velocity. It is generally known to measure the rotational speeds of shafts by applying, circumferentially on the shaft, an encoder in the form of a periodic pattern, for example a toothed wheel, which is sampled by a sensor applied in a stationary manner next to the shaft. The sensor has the capability of distinguishing a tooth and tooth gap or other periodically varying properties or physical quantities, for example magnetic field direction or optical transparency. The sensor thereupon generates an output signal, which has the same periodicity as the sampled pattern.
When, in connection with a rotational speed/angular velocity measurement or speed measurement, an absolute position or an absolute angle needs to be identified, it is known to use a separate additional system which, instead of the periodic pattern, has an index marking or a plurality of index markings. When the index marking is identified by the separate system, the sensor is at the index position, that is to say a position or an angle whose absolute value is known. The overall system can determine all subsequent positions or angles by recording the change starting from the index position with the aid of the periodic pattern.
For cost reasons, however, for example for applications in motor vehicles, a separate system for identifying an absolute position is often avoided even though an absolute measurement is necessary. Then, the periodic pattern of the system used for the angular velocity/speed measurement is interrupted at a position. From the interruption of the otherwise periodic signal sequence, the index position can thus be deduced. A prerequisite for this is merely limitation of the acceleration, or angular acceleration, so that an interruption of the signal sequence at the index position can be distinguished from the regular sequence with the greatest delay. This is generally the case in technical applications owing to the inertia of the system, or may readily be induced by selection of the parameters of the periodic pattern.
As mentioned, the periodic structure of the single encoder must be interrupted at a position in order to avoid the costs of an additional system. This is usually done by omitting the periodic structure for two periods, for example by means of two missing teeth in the series of teeth. The index position can thereby be identified reliably. For the frequency measurement which is necessary for the angular velocity/speed measurement, however, a new problem arises since the frequency is now temporarily broken and an interpolation or extrapolation method is needed in order to be able to measure the frequency over the index position, without the index marking making a false contribution.
An interpolation is sufficient if the signal is to be output with a delay. In the case of undelayed output, an extrapolation is necessary.